By means of a phenomenological model of weak-field thermoremanent magnetiza
tion (TRM) it is possible to reproduce the complex behaviour of TRM and par
tial TRM (pTRM) to a good approximation. The model depicts a sample as a co
llection of statistically independent magnetization elements, each of which
possesses a definite blocking and a definite unblocking temperature. Moreo
ver, for weak fields, linear dependence of remanence on applied field is as
sumed for each magnetization element. These assumptions are sufficient to d
erive to first order the experimentally found relations between the differe
nt types of pTRMs. The kinematic equation, which is assumed to govern the c
ooling process in multidomain (MD) material, is obtained from the model whe
n mean-field interaction is taken into account. The phenomenological model
is supported by two physical approaches. Using magnetic phase theory the co
efficients that occur in the kinematic equation as derived from the phenome
nological model can be physically interpreted for an isotropic ensemble of
uniaxial MD particles. A rigorous micromagnetic analysis of the thermal equ
ilibrium state proves the linearity of equilibrium remanence as a function
of a weak applied field. A statistical argument extends this linearity to w
eak-field TRM, which may be carried by non-equilibrium states.